My Psycho did what your Killer does. Also he would run across the room and attack you without warning. One Christmas he took off and tried to run up the Christmas tree and knocked it down - twice. But, sadly he dashed in front of a car and was killed.
My Psycho will be cuddling with you and all of a sudden just bite you and run away.
She was also raised with my Rottweiler, Darling Precious, who loved her. They would cuddle together and then Psycho would whap her on the head three times and run away.
I have a picture of the two of them together - I'll try to find it.